Measuring the Information Density of Interlanguage: An Entropy Analysis

Interlanguage development is often assessed through structural counts that only partially capture how learner language is organized probabilistically. This study proposes a multi-level framework for measuring interlanguage information density using entropy-based metrics. A corpus of 150 L2 English argumentative essays from B1, B2, and C1 learners was compared with a genre-matched native-speaker corpus of 50 essays. Four indicators were examined: lexical entropy (Hₗₑₓ), grammatical divergence from a native reference distribution via POS trigrams (KL₍gram₎), compression ratio (CR), and positional concentration index (PCI). To model native variability more defensibly, KL₍gram₎ for each L1 text was calculated against a leave-one-out L1 reference distribution. Results showed a clear developmental gradient: lexical entropy and positional concentration increased with proficiency, whereas grammatical divergence and compression ratio decreased. Mixed-effects models confirmed that these shifts were robust effects of proficiency. The findings support a probabilistic view of interlanguage development and offer a principled diagnostic framework for evaluating communicative efficiency in L2 writing.